# Calculating expressions to the power of two with radicals

How do we calculate $(2\sqrt{22})^2$?

I tried but failed: $$2*2+2*\sqrt{22}+ \sqrt{22}*2+\sqrt{22}*\sqrt{22}$$ The answer is 88. Thanks!

• This is not $(a+b)^2$ but $(a\times b)^2$ – Claude Leibovici Feb 27 '15 at 9:53
• $(2\sqrt{22})^2=2\sqrt{22} \times 2\sqrt{22}=2 \times 2 \times \sqrt{22} \times \sqrt{22}=4\times 22=88$,see Claude's comment for your mistake – Vikram Feb 27 '15 at 10:06

When you see an expression like $ab$, it means $a\cdot b$, not $a+b$. Thus
$$2\sqrt{22}\equiv 2\cdot\sqrt{22},$$
and there's no need to distribute multiplication $a^2=aa$ over factors of $2$ and $\sqrt{22}$. Distribution is only needed over terms of a sum, not product.